I know how to work this problem for instantaneous deployment. However, if the deployment is non-instantaneous, I need to make a few assumptions. The first is that the area of the parachute increases linearly with time: A(t) = A0 + kt, where A0 is the initial area of the undeployed parachute and k is the time rate of area increase.
***What should I assume for A0???
***Is it reasonable to assume that the parachute can be deployed in 3-5 seconds? Is this too great a time interval? Too small? From this I can determine the approximate value of k (area increase per second).
***I was told I can assume the coefficient of drag remains constant.

Does this sound like a reasonable model for non-instantaneous deployment? If so, I know how to find the desired values for distance and velocity. Am I on the right track???